Le 13-juil.-05, à 06:02, Russell Standish a écrit :

Complex numbers indeed do not have an ordering (being basically
   points on a plane)

So you pretend the axiom of choice is false. It is easy to build an ordering of the complex numbers through it.

There is no ordering *which satisfies some algebraic desiderata*. But as a set, you can always ordered it (given that the axiom of choice is consistent with ZF).



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